带有非局部条件的1<β≤2分数阶脉冲积分-微分发展方程温和解的存在性和存在唯一性  

Existence and uniqueness of mild solutions for fractional impulsive integro-differential evolution equations of order 1<β≤2 with nonlocal conditions

作　　者：刘立山[1] 秦海勇 Lishan Liu;Haiyong Qin

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]齐鲁师范学院数学学院,济南250200 [3]山东大学控制科学与工程学院,济南250061

出　　处：《中国科学：数学》2020年第12期1807-1828,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871302)资助项目。

摘　　要：本文研究带有非局部条件的1<β≤2分数阶脉冲积分-微分发展方程温和解的存在性和存在唯一性.在预解算子非紧和紧两种情形下,利用(广义) Darbo不动点定理和Schauder不动点定理建立了温和解的存在性结果.同时,利用(广义) Banach压缩映像原理,给出了温和解的存在唯一性结果.这些结果主要利用半群理论、预解算子定理、非紧性测度和不动点定理获得.最后给出一个例子来说明主要结果的有效性.This paper investigates the existence and uniqueness of mild solutions for fractional impulsive integrodifferential evolution equations with nonlocal conditions of order 1<β≤2.Under two cases where the solution operator is compact and noncompact respectively,the existence results of mild solutions are established by the(generalized) Darbo fixed point theorem and Schauder fixed point theorem.Meanwhile,uniqueness of mild solutions is also given by the (generalized) Banach contraction mapping principle.These results are obtained by the semigroup theorem,solution operator theorems,measures of noncompactness and fixed point theorem.At last,an example is presented to illustrate the effectiveness of the main results.

关 键 词：分数阶脉冲积分-微分发展方程 非紧性测度 预解算子 温和解 存在性和存在唯一性 

分 类 号：O175[理学—数学]